Model studies of long Josephson junction arrays coupled to a high-Q resonator

Series‐biased arrays of long Josephson junction fluxon oscillators can be phase locked by mutual coupling to a high‐Q, linear distributed resonator. A simplified model of such a device, consisting of junctions described by the particle‐map perturbation theory approach which are capacitively coupled to a lumped, linear tank circuit, reproduce the essential experimental observations at a very low computational cost. A more sophisticated model, consisting of partial differential equation descriptions of the junctions, again mutually coupled to a linear tank, substantially confirm the predictions of the simplified model. In the particle‐map model, the locking range in junction bias current increases linearly with the coupling capacitance; in the partial differential equation (p.d.e.) model, this holds up to a certain maximum value of the capacitance, after which a saturation of the locking range is observed. In both models, for a given spread of junction lengths, the existence of a minimum value of the capacitance for locking to a tank with a given resonant frequency is evidenced

Resonant Steps in the Characteristics of a Josephson Junction Coupled to a Transmission Line

A novel circuit is described which functions as an electronic analog of lumped element transmission line. The circuit requires only operational amplifiers, resistors, and capacitors. This module was coupled to a Josephsonj unction simulator and current voltage characteristics of the combined system were recorded. Steps were observed at voltages determined by the appropriate line resonances. When the transmission line was terminated with loads less than the characteristic impedance, chaos was seen in the lower steps. Similar results were obtained by numerical integration of the corresponding system of differential equations

Dynamical Properties of Josephson Junctions Coupled by a Transmission Line

A system composed of two Josephson junctions connected by a transmission line has been studied by means of electronic analog simulation. Under external current bias, the resistive component of the coupling induces frequency locking between the two junctions at commensurate ratios. The resonant modes of the transmission line give rise to steps in the I-V characteristics of the system